Publikation:

The permanence of R-boundedness and property(alpha) under interpolation and applications to parabolic systems

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Kaip_Saal_interpolation.pdf
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2011

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http://nbn-resolving.de/urn:nbn:de:bsz:352-165994
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Zusammenfassung

This note consists of two parts. In the first part we consider the behavior of R-boundedness, R-sectoriality, and property(α) under the interpolation of Banach spaces. In a general setting we prove that for interpolation functors of type h the R-boundedness, the R-sectoriality, and the property(α) preserve under interpolation. In particular, this is true for the standard real and complex interpolation methods. The second part represents an application of the first part. We prove R-sectoriality, or equivalently, maximal Lp-regularity for a general class of parabolic systems on interpolation spaces including scales of Besov- and Bessel-potential spaces over Rn.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Interpolation von Banachräumen, R-Beschränktheit, maximale Regularität, parabolische Systeme

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ISO 690SAAL, Jürgen, Mario KAIP, 2011. The permanence of R-boundedness and property(alpha) under interpolation and applications to parabolic systems
BibTex
@unpublished{Saal2011perma-16599,
  year={2011},
  title={The permanence of R-boundedness and property(alpha) under interpolation and applications to parabolic systems},
  author={Saal, Jürgen and Kaip, Mario}
}
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    <dcterms:abstract xml:lang="eng">This note consists of two parts. In the first part we consider the behavior of R-boundedness, R-sectoriality, and property(&amp;#945;) under the interpolation of Banach spaces. In a general setting we prove that for interpolation functors of type h the R-boundedness, the R-sectoriality, and the property(&amp;#945;) preserve under interpolation. In particular, this is true for the standard real and complex interpolation methods. The second part represents an application of the first part. We prove R-sectoriality, or equivalently, maximal Lp-regularity for a general class of parabolic systems on interpolation spaces including scales of Besov- and Bessel-potential spaces over Rn.</dcterms:abstract>
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